What are the odds of rolling the same roll three times in a row ? I know 1/36 for each roll, but 3 in a row?

Question

I play backgammon at a website that swears up and down that the number generator is random. However, in nearly every game I play, I get back to back rolls, and often the same roll 3 in a row. I have no data whether this should be commonplace and would appreciate some help. The probability of any one roll is 1/36, although many rolls can be accomplished more than one way ... however, sincerely, what are the odds of 2 or 3 in a row.  Anyone ?

Josh S · Accepted Answer

Well, if you are talking about doubles (1,1), (2,2) the odds of 2 in a row are

(1/36)^2 = 1 in 1296

for three in a row, its (1/36)^3 = 1 in 46656

If you are talking about stuff like (5,2), this is the same as (2,5), so the odds of that specific roll is really 1/18. In which case odds for more than one in a row is

(1/18)^2 = 324

(1/18)^3 = 5832

doug · Answer

For example you roll double 1's twice in a row its.
 For 2= 1296
 For 3= 1/46656

You can get a 7 in 7 differnt ways.
So the odds a way lower

bob · Answer

1 in 46656

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What are the odds of rolling the same roll three times in a row ? I know 1/36 for each roll, but 3 in a row?

3 Answers